Solve [5^2-(-2)^2-(-3)^2/(-3)(-2)]^3

$$[ \frac { 5 ^ { 2 } - ( - 2 ) ^ { 2 } - ( - 3 ) ^ { 2 } } { ( - 3 ) ( - 2 ) } ] ^ { 3 }$$

Evaluate

$$8$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{25-\left(-2\right)^{2}-\left(-3\right)^{2}}{-3\left(-2\right)}\right)^{3}$$

Calculate -2 to the power of 2 and get 4.

$$\left(\frac{25-4-\left(-3\right)^{2}}{-3\left(-2\right)}\right)^{3}$$

Subtract 4 from 25 to get 21.

$$\left(\frac{21-\left(-3\right)^{2}}{-3\left(-2\right)}\right)^{3}$$

Calculate -3 to the power of 2 and get 9.

$$\left(\frac{21-9}{-3\left(-2\right)}\right)^{3}$$

Subtract 9 from 21 to get 12.

$$\left(\frac{12}{-3\left(-2\right)}\right)^{3}$$

Multiply -3 and -2 to get 6.

$$\left(\frac{12}{6}\right)^{3}$$

Divide 12 by 6 to get 2.

$$2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$8$$

Factor

$$2^{3}$$